Problem: Solve for $x$ and $y$ using elimination. ${-4x-3y = -64}$ ${3x-5y = -10}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $4$ ${-12x-9y = -192}$ $12x-20y = -40$ Add the top and bottom equations together. $-29y = -232$ $\dfrac{-29y}{{-29}} = \dfrac{-232}{{-29}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-4x-3y = -64}\thinspace$ to find $x$ ${-4x - 3}{(8)}{= -64}$ $-4x-24 = -64$ $-4x-24{+24} = -64{+24}$ $-4x = -40$ $\dfrac{-4x}{{-4}} = \dfrac{-40}{{-4}}$ ${x = 10}$ You can also plug ${y = 8}$ into $\thinspace {3x-5y = -10}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(8)}{= -10}$ ${x = 10}$